A Note on Strongly Starlike Mappings in Several Complex Variables. (3rd March 2014)

• Record Type: Journal Article
• Authors: Hamada, Hidetaka; Honda, Tatsuhiro; Kohr, Gabriela; Shon, Kwang Ho
• Other Names: Choi Junesang Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-03-03
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/265718
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Let f be a normalized biholomorphic mapping on the Euclidean unit ball 𝔹 n in ℂ n and let α ∈ 0, 1 . In this paper, we will show that if f is strongly starlike of order α in the sense of Liczberski and Starkov, then it is also strongly starlike of order α in the sense of Kohr and Liczberski. We also give an example which shows that the converse of the above result does not hold in dimension n ≥ 2 .